What is the motivation behind static polymorphism in C++?

What is the motivation behind static polymorphism in C++?

I understand the mechanics of static polymorphism using the Curiously
Recurring Template Pattern. I just do not understand what is it good for.
The declared motivation is:
We sacrifice some flexibility of dynamic polymorphism for speed.
But why bother with something so complicated like:
template <class Derived>
class Base
{
public:
void interface()
{
// ...
static_cast<Derived*>(this)->implementation();
// ...
}
};
class Derived : Base<Derived>
{
private:
void implementation();
};
When you can just do:
class Base
{
public:
void interface();
}
class Derived : public Base
{
public:
void interface();
}
My best guess is that there is no semantic difference in the code and that
it is just a matter of good C++ style.
Herb Sutter wrote in Exceptional C++ style: Chapter 18 that:
Prefer to make virtual functions private.
Accompanied of course with a thorough explanation why this is good style.
In the context of this guideline the first example is good, because:
The void implementation() function in the example can pretend to be
virtual, since it is here to perform customization of the class. It
therefore should be private.
And the second example is bad, since:
We should not meddle with the public interface to perform customization.
My question is:
What am I missing about static polymorphism? Is it all about good C++ style?
When should it be used? What are some guidelines?